Greatest Common Factor of 16, 28 and 36 by Prime Factorization

Given Numbers: 16, 28, 36
Identify the Prime Factors of 16, 28 and 36 by Prime Factorization

• Prime Factorization of 16: 16 = 2 x 2 x 2 x 2 = 2⁴
• Prime Factorization of 28: 28 = 2 x 2 x 7 = 2² x 7¹
• Prime Factorization of 36: 36 = 2 x 2 x 3 x 3 = 2² x 3²

Determine the Prime Factor(s) that are common to the Prime Factorization of each number:

• 2 is the only Prime Factor common to the Prime Factorizations of 16, 28 and 36

Determine the least number of occurrences of 2 among the Prime Factorizations:

• 2 occurs at least 2 times in each Prime Factorization

As a result, the Greatest Common Factor (GCF) of 16, 28 and 36 is equal to 2 x 2, which equals 2 raised to the power of its least number of occurrences or smallest exponent among the Prime Factorizations:

• GCF(16, 28, 36) = 2² = 2 x 2
• GCF(16, 28, 36) = 4

Therefore, the Greatest Common Factor of 16, 28 and 36 by Prime Factorization = 4